随机过程初级教程(英文版•第2版)
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图灵原版数学统计学系列

随机过程初级教程(英文版•第2版)

Samuel Karlin (作者)
终止销售
本书系统论述随机过程的基本理论和方法,理论与实际应用并重。书中主要内容有:马尔可夫链、连续时间马尔可夫链、更新过程、鞅论、布朗运动、分支过程和平稳随机过程。本书涉及范围十分广泛,含有丰富的背景知识,深入浅出,不需要测度论作为预备知识。
本书可作为高等学校本科生和研究生的教材,也可作为工程技术人员的参考书。
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出版信息

  • 书  名随机过程初级教程(英文版•第2版)
  • 系列书名图灵原版数学统计学系列
  • 执行编辑关于本书的内容有任何问题,请联系 傅志红
  • 出版日期2007-09-20
  • 书  号978-7-115-16598-5
  • 定  价69.00 元
  • 页  数572
  • 开  本16开
  • 出版状态终止销售
  • 原书名A First Course in Stochastic Processes
  • 原书号0-12-398552-8

同系列书

目录

Preface xi
Preface to First Edition xv
Chapter 1
ELEMENTS OF STOCHASTIC PROCESSES
1.Review of Basic Terminology and Properties of Random Variables and Distribution Functions 1
2.Two Simple Examples of Stochastic Processes 20
3.Classification of General Stochastic Processes 26
4.Defining a Stochastic Process 32
Elementary Problems 33
Problems 36
Notes 44
References 44
Chapter 2
MARKOV CHAINS
1.Definitions 45
2.Examples of Markov Chains 47
3.Transition Probability Matrices of a Markov Chain 58
4.Classification of States of a Markov Chain 59
5.Recurrence 62
6.Examples of Recurrent Markov Chmns 67
7.More on Recurrence 72
Elementary Problems 73
Problems 77
Notes 79
References 80
Chapter 3
THE BASIC LIMIT THEOREM OF MARKOV CHAINS AND PLICATIONS
1.Discrete Renewal Equation 81
2.Proof of Theorem 1.1 87
3.Absorption Probabilities 89
4.Criteria for Recurrence 94
5.A Queueing Example 96
6.Another Queueing Model 102
7.Random Walk 106
Elementary Problems 108
Problems 112
Notes 116
Reference 116
Chapter 4
CLASSICAL EXAMPLES OF CONTINUOUS TIME MARKOV CHAINS
1.General Pure Birth Processes and Poisson Processes 117
2.More about Poisson Processes 123
3.A Counter Model 128
4.Birth and Death Processes 131
5.Differential Equations of Birth and Death Processes 135
6.Examples of Birth and Death Processes 137
7.Birth and Death Processes with Absorbing States 145
8.Finite State Continuous Time Markov Chains 150
Elementary Problems 152
Problems 158
Notes 165
Reference 166
Chapter 5
RENEWAL PROCESSES
1.Definition of a Renewal Process and Related Concepts 167
2.Some Examples of Renewal Processes 170
3.More on Some Special Renewal Processes 173
4.Renewal Equations and the Elementary Renewal Theorem 181
5.The Renewal Theorem 189
6.Applications of the Renewal Theorem 192
7.Generalizations and Variations on Renewal Processes 197
8.More Elaborate Applications of Renewal Theory 212
9.Superposition of Renewal Processes 221
Elementary Problems 228
Problems 230
Reference 237
Chapter 6
MARTINGALES
1.Preliminary Definitions and Examples 238
2.Supermartingales and Submartingales 248
3.The Optional Sampling Theorem 253
4.Some Applications of the Optional Sampling Theorem 263
5.Martingale Convergence Theorems 278
6.Applications and Extensions of the Martingale Convergence Theorems 287
7.Martingales with Respect to σ-Fields 297
8.Other Martingales 313
Elementary Problems 325
Problems 330
Notes 339
References 339
Chapter 7
BROWNIAN MOTION
1.Background Material 340
2.Joint Probabilities for Brownian Motion 343
3.Continuity of Paths and the Maximum Variables 345
4.Variations and Extensions 351
5.Computing Some Functionals of Brownian Motion by Martingale Methods 357
6.Multidimensional Brownian Motion 365
7.Brownian Paths 371
Elementary Problems 383
Problems 386
Notes 391
References 391
Chapter 8
BRANCHING PROCESSES
1.Discrete Time Branching Processes 392
2.Generating Function Relations for Branching Processes 394
3.Extinction Probabilities 396
4.Examples 400
5.Two-Type Branching Processes 404
6.Multi-Type Branching Processes 411
7.Continuous Time Branching Processes 412
8.Extinction Probabilities for Continuous Time Branching Processes 416
9.Limit Theorems for Continuous Time Branching Processes 419
10.Two-Type Continuous Time Branching Process 424
11.Branching Processes with General Variable Lifetime 431
Elementary Problems 436
Problems 438
Notes 442
Reference 442
Chapter 9
STATIONARY PROCESSES
1.Definitions and Examples 443
2.Mean Square Distance 451
3.Mean Square Error Prediction 461
4.Prediction of Covariance Stationary Processes 470
5.Ergodic Theory and Stationary Processes 474
6.Applications of Ergodic Theory 489
7.Spectral Analysis of Covariance Stationary Processes 502
8.Gaussian Systems 510
9.Stationary Point Processes 516
10.The Level-Crossing Problem 519
Elementary Problems 524
Problems 527
Notes 534
References 535
Appendix
REVIEW OF MATRIX ANALYSIS
1.The Spectral Theorem 536
2.The Frobenius Theory of Positive Matrices 542
Index 553
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